Global behavior of solutions to the static spherically symmetric EYM equations

Abstract

The set of all possible spherically symmetric magnetic static Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge group $G$ was classified in two previous papers. Local analytic solutions near the center and a black hole horizon as well as those that are analytic and bounded near infinity were shown to exist. Some globally bounded solutions are also known to exist because they can be obtained by embedding solutions for the $G=SU(2)$ case which is well understood. Here we derive some asymptotic properties of an arbitrary global solution, namely one that exists locally near a radial value $r_0$, has positive mass $m(r)$ at $r_0$ and develops no horizon for all $r>r_0$. The set of asymptotic values of the Yang-Mills potential (in a suitable well defined gauge) is shown to be finite in the so-called regular case, but may form a more complicated real variety for models obtained from irregular rotation group actions.

43 pages

References in corpus (4)

• Rotating Hairy Black Holes
• On the linear stability of solitons and hairy black holes with a negative cosmological constant: the odd-parity sector
• Static axially symmetric solutions of Einstein-Yang-Mills equations with a negative cosmological constant: the regular case
• On all possible static spherically symmetric EYM solitons and black holes

Cited by in corpus (5)

• Classical Yang-Mills black hole hair in anti-de Sitter space
• Soliton and black hole solutions of su(N) Einstein-Yang-Mills theory in anti-de Sitter space
• Static Spherically Symmetric Solutions of the SO(5) Einstein Yang-Mills Equations
• Spherical symmetry of generalized EYMH fields
• There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models